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Nature's String Stitching Device for the Production of a Language Space 

Bernhard Bierschenk 

Department of Psychology 

Lund University 

Copenhagen Competence Research Centre 

University of Copenhagen 

Poster session presented at 9^^ Herbstakademie on Self-Organisation of Cognition and 
Applications to Psychology, Conference on Dynamical Systems in Cognitive Science, October 
25-28, 2000, Ascona, Monte Verita, Switzerland. 


No one has ever been able to look into the language space nor has anyone been able to 
measure the phenomenon of consciousness without the interference of an observer. This 
article is changing this situation completely. From now on it is possible to produce measures 
of consciousness without the presence of classical observation devices. In particular, the 
observation problem can be bypassed since the "observer" is part of the "observed". This 
means that the phenomenon is describing itself. Since there is no longer any need for 
mirroring the state of consciousness by the state of an apparatus, the classical problem of an 
observation on the apparatus has disappeared. It is shown that the measurement situation has 
been changed fundamentally. A full description is attainable through the establishment of the 
geometrical shapes of involuted textual flows. 

The Axiomatic Foundation of the Steering and Control Mechanism 

A fundamental fact of all living systems is that they are "self-referential" and thus that 
they contain their own description. Further, in departing from the fundamental hypothesis that 
Nature is the producer of language, this hypothesis requires that the steering and control 
mechanism, responsible for proper production becomes recognisable. From a strictly 
scientific point of view it is, however, not sufficient to take the point of departure in Nature. 
Methodological considerations have to be based on an a-priori assumption. In the present 
context, the assumed basic principle, underlying all living systems is the following: 

AaO—>' Axiom (1) 

The principle, stated in Expression (1) presupposes a dual steering and control mechanism, 
which is anchored in the A-0-dependency. Further, as the a-priori principle of all living 
systems, it is the foundation for the establishment of "synthesis " and consequently meaning. 
By this assumption, it is likewise stated that the principle is reflecting Natural Law. However, 
the reflection requires the introduction of a copy of the principle, which makes it functional: 

[AaO] -^ Functional Axiom (2) 

Hence, the functional axiom implies a copying process, which is establishing the biological 
mechanism underlying natural language production. By this assumption is meant that the 
principle becomes functional in the moment when a copy of its components is being realised. 
Functional in Expression (2) refers to the production of a "standard copy". Each time such a 
copy is being copied, the copying process is carried out irrespective of its meaning. 

However, from an evolutionary point of view, it can be stated that irreversible time 
enters into the process, which makes the mechanism always departing from any strict or 
uniform reproduction. Hence, the mechanism steadily is producing new forms of expression. 
This circumstance is symbolised in Expression (3): 

[0a0] -^ Incompleteness (3) 

When either the A-component or the 0-component of the dual steering and control 
mechanism is missing at the textual level, incompleteness is to hand. It would not be out of 
place to mention that Expression (3) has far-reaching consequences for the study of language 
as a phenomenon of nature. 

Except that the duplication, according to Expression (2) takes place in strictly 
mechanical terms, the co-operative interaction between different A's and O's is producing 
various displacements of the components through their "dislocation ". This condition is 
symbolised as follows: 

[Aa(0Aa0o)] -^ Interacting Sequence (4) 

Hence, through dislocation of different components in the order of succession, every new 
language expression is establishing itself as a new form and the result of novel terminal states. 
When the language production process is ordering the copies in interacting sequences, 
irreversible time is governing the process, but this requires that some copies emerge 
incomplete. This circumstance is influencing profoundly both the evolutionary process that 
generates radical flow morphologies and the "channelling" of the flows, which requires that 
channels are swiftly formed in order to transport the corresponding textual flows. 

Establishment of Completeness 

To be able to identify the A-component presupposes that its identity can be 
discovered, which is possible only under the condition that a text producer writes something. 
Getting to know the A-component this way implies that an action becomes real and that its 
linguistic expression reflects the nature of the action, which is the production of a strict A-0- 
dependency. However, it is crucial to be able to catch the corresponding movement at the 
textual level, which is carried out as follows: 

Figure 1. 

Establishment of Completeness 

Verb absent 

Curling String 

Verb present 

of Strict 

The "curling string" of Figure 1 demonstrates a first measure in the development of a 
language space. Successful development builds on the identification of the verbs present. 
Without the presence of a verb no channels can be formed. On the other hand their presence is 
establishing the ways in which the A's and O's contribute to the development of a space. 
Hence, the a-component is determining the specific bonding relations, which the participating 
verbs have produced. 

The curling string. The production of a language space and its effect on developing 
flow morphologies becomes accessible only if a complete textual surface can be produced. 
Such a surface requires that the dummies can be supplemented with text segments, i.e., sewed 
up. But this operation can only be performed under the condition that there is either a thread 
or a string with which the mechanism can work. Therefore, their production and use must 
necessarily refer to intentionality (int) as well as orientation (ort). This means at the same time 
that dimensionality is inherent within the string itself. Further, it becomes identifiable and 
differentiable in the moment when a grapheme is produced. Hence observing the production 

of natural language expressions in a meaningful environment is hardly possible without an 
intention and orientation. Figure 1 presupposes that the intention can be separated from the 
orientation. It follows that a grapheme is a suitable marker of an identifiable string. Any string 
may be associated with some of the components (A, O) and give expression to the variability 
within each component. The difference of this variability may refer to variance in the 
complexity of the strings on one hand and to the curling of the strings on the other, which 
express distance in place and time. 

The Ring Structure 

The intentional dimension is manifesting a fundamental fact of all living systems, 
namely to be able to stretch through the co-operative action (a) in order to be adaptive in 
relation to some objectives (O's). The second dimension indicates the importance of living 
system's ability to orientate toward a particular Objective (O). However, when the A's and 
O's reside in the same biophysical system (i.e., an organism), this system must be treated as 
self -referential. Its functional operations are demonstrated in Figure 2. 

Figure 2. 

Ring Structure 

Clause Markers (CM) 

Ring Structure 





Hence, natural language, conceived of as self -referential system, is organising itself and 
characterised by a biophysical mechanism, which is developing the structural aspect of a 
graphical expression in the form of a grapheme and strings of graphemes. It follows that a 
ring structure is always open to expansion before it is absorbing textual elements. In its 
function, it is performing either as an indicator of structural relations or as a communicative 
tool when it is forming the channels of the textual flow. In its latter function, it is always a- 
posteriori and regulative. But both functions contribute to the development and shape of the 
language space. 

As shown in Figure 2, in case there is a dummy of one or the other type, this means 
that a textual flow is observable, which is concentrated to those places where the dummies 
have emerged. As to the channel formation, the dummies mark "holes" in the textual surface, 
which implies that they may be used to decide upon the character of a particular flow 
morphology, resulting from the corresponding textual pattern dynamics. Finally, the triangle 
of Figure 2 marks that two copies have been coupled on the vertical axis. Vertical coupling is 
a mark of spiralling structure as well as an indication of an evolving configuration, which is 
the result of a "winding factor" (Winfree, 1980). 

The mechanism, obviously, operates in accordance with a pendulum. In its forward or 
downward move, textual segments are driven into those places, where text is missing. But in 
the backward or upward move of the pendulum, explicitly integrated textual segments are 
moved into places, where they stay permanently. It follows that pendular movements create 
accelerations in textual flows, which are directed toward centres, where the involved textual 
elements become strongly concentrated. 

But even more important is the fact that the pendulum obeys two laws. One requires 
the mechanism to keep and conserve the strict dependency, which must hold within the A-0- 
pairs. The other requires that the pendulum always is establishing symmetry. Together, the 
two laws lead to strict co-ordination, which results in the establishment of "blocks". The 
"block" concept concerns synchronisation. This means that an A-O-pair within a block 
remains both co-ordinated and unchanged when exposed to different phase transitions. As 
may have become evident, a textual agent and a textual objective give expression to a 
dynamics, which comes about within strict borderlines. Thus far, involved phase 
dependencies are marked by the "Clause Markers" (CM), which are interlocking the 
thermodynamic patterning. 

Irreversible Time 

As a minimum, a block is an expression of both displacements in equal steps and 
firmness in its evolutionary development by known and unknown order parameters. In 
addition, block-wise operations do not allow whether a rhythmic or a clock-like rotation 
within individual components. A liberalisation of the movement patterns of the components 
would imply that every single component within the pair is following its own autonomous 
rhythm. By handling this individuality, the system has been capable of establishing two 
autonomous clocks (the black dots), namely an A-clock governing the A-component and an 
0-clock governing the 0-component. Figure 3 is demonstrating the clocking mood of the 

Characteristic of the co-operativity of the clocks is that the angle from one to the other 
is captured in the exponential relation (e'^), where (i) specifies the intentional plane of the 
angle of rotation, while (|0|) specifies the magnitude of the angle and the straight brackets 
denote the absolute value of the operation. When a certain number of rotations through the 
angles have been processed, the result appears as "multiplicative redundancy". 

Figure 3. 

The Clocking Mood 


A = (^=180° 

= 6=180'^ 

= ^1 

Irreversible Time 

=[(0- (V(^2 + ^62)] 

The Ring-Structure 

A Researcher 

a observed 

0o [infants + on the cliff] 

CM that 


A infants 

a crawled 

O on the cliff 

According to Hestenes (1993, p. 68), this condition can be expressed as [(e'^ e"t')=e''^^^'l'^= e"'' 
e'^], which follows from Moivre's theorem [e'^''l')"=e'"^''l'] . However, the exponential function 
and its series expansion require that angles become measured in radians (Hestenes, 1993, p. 

Related to the text example, it is easily demonstrated that the A-clock in the case of 
the first clause is initiating a work cycle with a spin of (-Vi). The same operation applies to the 
A-component of the second clause. However, the 0-clock is initiating work-cycles of 
different kinds. While the 0-clock in the second clause likewise performs a work cycle of a 
spin of (-Vi), its operation in the first clause is clearly of a different kind, since the co- 
ordinative dependency between the clauses is initiating a work cycle with a spin of (-2). 

Expressed in geometrical terms, the meaning of the involved rotations is the 
following: The 0-clock first moves one turn counter-clockwise and is thereby establishing 
zero degrees for the empty place (marked by the dummy). Thereafter, the clock is initiating 
another turn to mark that the empty place will be filled with a complete functional clause (i.e. 
the second clause). Since the entire clause constitutes unity (360°), the second turn leads to 
the establishment of (360°) for the dummy. However, Figure 3 has shown that the involved 
pendulum moves both components counter-clockwise and in the same direction to eliminate 
the implied zero point of the first clause. 

This operational prerequisite is describing a shadow-like movement, which is 
indicated by the grey tint of the spot. This condition has to get its operational expression, 
which means that the original articulation is reduced by the square root of the components, 
respectively. It follows that the roots of the copied components are subtracted from the angle 
of articulation at the reference point. This procedure serves perfectly the expression of the 
implicit parts of a textual flow. 

A conclusion to be drawn from Figure 3 is that the rotation of strings of graphemes is 
driving the rhythmically operating work cycles in the direction toward the sharpest increase in 
acceleration. Once again, the displacements of grapheme strings can be updated and the 
change in angular articulation can be calculated without intervening disruptions. Through the 
clocking mood of the pendulum, it is possible to denote corresponding increases, which 
finally carry structural significance. Structural significance is addressing the fact that the 
present approach has not had any use of "free parameters". From a functional point of view, it 
means that the approach is not fitted into one or the other empirical context. Thus, this fact 
may be used as a valid basis for an unambiguous and definitive test of the validity of the 


In the text example in Figure 3 is the dummy (0) symbolising some environmental or 
contextual variable, which may be an object or event. In this case it is an event, which 
incorporates an Agent and an environment. The relation between the two Agents is 
asymmetrical in the sense that the second Agent is experiencing an unknown environment, 
while the first Agent already is "knowing" the environment through integrated experiences. 
Consequently, in his observations (as reported verbally) the knower is always present in the 
known. Thus, the thesis is that knowing is the result of an active inquiring agent (the knower). 
Gibson (1979, pp. 156-158) makes the corresponding assumption when he is experimenting 
with the "Visual Cliff. 

As exemplified by the picture series of the Visual Cliff experiments (Gibson & Walk, 
1960), the formalism proposed transforms the organism and the environment through a twist 
into cognition. Thus, inherent in the process of communication is the process of transforming 
meaningful behaviour into symbolic expressions. At this level, the transformation entwines 

the perspective and viewpoints in the same way as organism and environment are entwined at 
the preceding level of processing. The structure embedded in the caption to the picture series 
may be visualised as a complementary arrangement of its components in a three-dimensional 
space. The process, anticipated to operate in this structure, will be demonstrated in Figure 4. 

Figure 4. 

The Design of the Visual Cliff 


-+ a 

- + 


(Centre Board 



(End of 




The manipulation of the action component of Figure 4 is manifesting itself through a binding 
of the values (-,+) to the A and O components respectively. Binding these values with respect 
to the complementary roles of A and O gives the events described by the picture series of 
Gibson and Walk (1965, p. 65). All pairings possible in the described event space are (— , -+, 
+-, ++) and the change of information in the picture series can be studied except for the first 
combination of symbols. A functional fixation of both organism and environment means 
sensation and is establishing the zero-hypothesis of perception. The first measure carried out 
is a fixation of the A-component representing the organism to which the value (-) is bound. 
The second measure implies a binding of the value (-) right adjusted. The top left picture of 
the Visual Cliff series is depicting the result (— ): A child is placed on the centre of the board. 

Gibson's ecological theory of perception presumes that the development of meaning 
be dependent on the viewpoints being changed. The third measure then implies mobilising the 
0-component to which the value (-I-) is bound. More than one viewpoint of the same kind may 
be observed. No change of perspective is implied. The result (-+) is made visible by the top 
right picture: The child crawls to its mother across the "shallow" side. Moreover, it is 
presumed that the observer's perspective can be viewed from various angles. By mobilising 
the A-component and by fixating the 0-component (-i--), a change in perspective is observed. 
The bottom left picture is documenting the result: Called from the "deep" side, the child pats 
the glass. The final relationship, to be described, can be observed by mobilising both the A- 
and the 0-component (-i-i-). The result implies maximal information synthesis, which is 
pictured bottom right: The inferred behaviour is that the child refuses to cross over to the 

The relation (— , -i-i-) and (--i-, -i--) is complementary to each other. This aspect is 
indicated by the two contrasting profiles. However the double asymmetry gives every pair a 
certain control over the development of every other and awareness is determined by re- 
orientation. Basically the asymmetrical pairs constitute the mechanism for a judgement of 
one's own possibility to come to solutions allowing an adaptation to fundamental changes. 


The Language Space of the Caption to the Visual Cliff Pictures 

It is commonly agreed upon that language is a more abstract level of processing than is 
vision. Nevertheless, a linguistic analysis has to be able to show the language space and to 
pick up the ecological invariants of this space, although using language- specific instead of 
vision- specific cues. Based on the caption it is discussed in what way verbal descriptions and 
textual transformation mediate the integration of experience as invariant structures. The 
caption is worded as follows: 

"CHILD'S DEPTH PERCEPTION is tested on the Visual Cliff. The apparatus 
consists of a board laid across a sheet of heavy glass, with a patterned material directly 
beneath the glass on one side and several feet below on the other. Placed on the centre board 
(top left), the child crawls to its mother across 'the shallow side' (top right). Called from the 
'deep' side, he pats the glass (bottom left), but despite this tactual evidence that the 'cliff is in 
fact a solid surface, he refuses to cross over to the mother (bottom right)." 

Language Space as Function of Textual Movement Production 

Whenever observational events structure the language of the observer, this language 
contains textual movement information, belonging to these events. Therefore, it is assumed 
that the mechanism has the capacity to reproduce the language space as it is evolving during 
the generation of the caption. 

The unfolded space of the Objective-component. Figure 5 shows the space of the 
textual objectives. The "objectives/interval" shows the number of objectives (i.e., the sliding 
within a particular interval), whereas the "intervals" are characterising the naturally occurring 
periods and fractions of periods the way they have become manifest during text production. 
The "dynamics", as measured in radians is visualising the accelerations in the rotations as 
well as temporary reductions. To convert the corresponding scatter plots to mesh plots, the 
grids have been interpolated with its standard transformation function of SigmaPlot (1998, pp. 
290-292). Version 5.0 of SigmaPlot is using an inverse distance method, where the distance 
weight value (p) has been set as (p = 3). Obviously, an unfolding operation entails the concept 
of time and its expression through successively increasing and decreasing shades in 

Some outstanding features of the response surface have been marked with 
corresponding textual elements. The empirical relations of the Objective-component seem to 
have been packed in such a way that their informational value can be detected. What is 
substantial and consequently explicit is related to the mother, the shallow side and the cliff. 
However, the insubstantial and consequently implicit specification of "change" is shown 
below sea level. The discontinuity in the information flow is marked with the corresponding 
textual elements, which relate to the deep and the deep side. 

The unfolded Space of the Agent-component. Figure 6 depicts the space of the textual 
agents. By making explicit reference to "tactile evidence", "the child" and "the child's 
perception" the process in the Agent-component refers to the organism as context for the 
manifestation of the nature of change. The "unknown" agents (X) are deeper embedded and 
appear as a matter of fact as implicit and independent of any implications as to context or 
contents that can be described in terms of sensational attributes. Hence, the informational 
invariants of the established spaces are assumed to reflect the ecologically significant aspects 
of the caption. 


Figure 5. 

The Unfolded Space of the Objective Component 

The Unfolded 0-Space 




Figure 6. 

The Unfolded Space of the Agent-Component 

The Unfolded A-Space 

Configuration of Informational Invariants as Function of Constraining Space 

The detection of "negative affordances" (Gibson, 1979, p. 157) is in the focus of the 
caption. However, the implicitness of the experimenters' reason in the caption is manifested 
below sea level in the child's "Capacity" to test the glass surface for its solidity. Obviously, 
the intention on the simulated cliff is stretching over a series of textual movements. These are 
folding and producing the synthesis of the caption, which implies its alternative description. 
The folded space of the Objective-component. The structured configuration of the O- 
space is shown in Figure 7. It concerns the judgement of "Depth" and its consequences for 
locomotion on the deep side. Synthesis entails that the variety of the involved textual elements 
becomes specified through terminological profiling. 


Figure 7. 

The Folded Space of the Objective-Component 

The Folded 0-Space 

Obviously, the transformational impact of the child's optical information processing is 
brought to the fore by the three termini "Meaning", Awareness", and "Hesitation". 
Apparently, the child's grasping of the meaning of a sharp drop has been verbalised 
successfully. Moreover, the special character and significance of an abrupt changing 
environment has been related successfully to the dangerous cliff. 


Figure 8. 

The Folded Space of the Agent-Component 

The Folded A-Space 


The folded Space of the Agent-component. As indicated by Figure 8, the occurring 
structure gives evidence to a stressful situation. The caption of the pictured procedure gives 
expression to the child's experience of a provocation. Its description through the produced 
termini makes visible that the terminus "Refusal" is the theoretically important global state 
attractor, since its name relates the concept of avoidance as its behavioural ground to the 
falling-off place of the virtual cliff. The environmental condition in the caption has been 
formulated in terms of a pertinent change. However, in order to investigate into the 
"Capacity" of the child to perceive directly the "Meaning" of the cliff, the caption is giving 
expression to "Doubt" and "Uncertainty". Both seem to be rooted in the child's experience 
of stressfulness. 



The central idea of studying the caption to the original Visual Cliff experiments has 
been to determine the capacity of the experimenters to communicate the knowledge they 
gained of the effects of the simulated environment. Independent of the degree to which they 
have been able to formulate it, it has to be communicated through natural language 
expressions, if it shall become knowable for both the experimenters themselves and for the 
scientific community at large. 

The basic hypothesis of the experiment has been that a subtle interplay between the 
oscillation of strings and the winding of work cycles is creating the language space. Thus this 
hypothesis concerns the capacity of the stitching mechanism to handle the subtle distinctions 
that are created by the textual strings in the process of producing space. At the same time the 
space hypothesis relates to the fact that the evolving space is restricting the movements of the 
strings. From the point of view of the experiment, this hypothesis implies that a verbal 
expression is suitable for processing, provided that it contains cues to its capacity of stretching 
and straining, and of winding and bending. So, a verbal material has to respond in an elastic 
way to the evolving dynamic of textual patterns. It is therefore not a coincidence to suggest 
that a text material must be characterised by flow properties and that these are decisive for the 
rotational dynamic, and consequently for the textual space being realised. 

A consequence of this requirement has been the characterisation of the loss of stability 
in a text. By this is meant that a scientific study of language as a natural phenomenon must 
begin with an observation of such losses of stability - in other words a study of discontinuity. 
Accordingly, an exact characterisation and formal description of cycles of "writing - reading 
- rewriting" have to be concentrated on a likewise exact characterisation and precise 
description of the phase transitions connected with the evolving textual space. Finally it is of 
crucial importance that a test of the basic experimental hypothesis builds on an uncovering 
and a reproduction of those kinds of order parameters that are restricting the production of a 
space. The described mechanism has this capacity and therefore, it has been possible to base 
the experiment on the following methodological properties: (1) manifestation of the 
acceleration in a rotation and (2) identification of the fundamental order parameters, which 
are governing the production of a space. 

Hence, the theoretical significance of the experiment lies in the determination of the 
phase transitions involved on the kinetic level and in the determination of the flow 
morphology of the text at different occasions of change. The changes at different phase 
transitions are of course influenced by the observations that the text producer has made and 
communicated. To communicate is a matter of realising both viewpoints as well as a 


Gibson, E. J., & Walk, R. D. (1960). The "visual cliff". Scientific American, 202(4), 64-71. 
Gibson, J. J. (1979). The ecological approach to visual perception. Boston, MA: Houghton 

Hestenes, D. (1993). New foundations for classical mechanics (Dordrecht: Kluwer Academic. 

(Original work published 1986) 
SigmaPlot 5.0. (1998). User's Guide. Chicago: SPSS Inc. 
Winfree, A. T. (1980). The geometry of biological time. Berlin: Springer Verlag. 

Correspondence and requests for materials should be addressed to Bernhard F. Bierschenk, 
Department of Psychology at Lund University, Paradisgatan 5P, S-223 50 Lund, Sweden. E-